William Hugh Woodin (born April 23, 1955) is an American mathematician and set theorist at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of highe ...

. He has made many notable contributions to the theory of

inner model In set theory, a branch of mathematical logic, an inner model for a theory ''T'' is a substructure of a model ''M'' of a set theory that is both a model for ''T'' and contains all the ordinals of ''M''. Definition Let L = \langle \in \rangl ...

s and

determinacy Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and si ...

. A type of

large cardinals In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least ...

, the Woodin cardinals, bear his name.

Biography

Born in Tucson,

Arizona Arizona ( ; nv, Hoozdo Hahoodzo ; ood, Alĭ ṣonak ) is a state in the Southwestern United States. It is the 6th largest and the 14th most populous of the 50 states. Its capital and largest city is Phoenix. Arizona is part of the Fou ...

, Woodin earned his Ph.D. from the University of California, Berkeley in 1984 under

Robert M. Solovay Robert Martin Solovay (born December 15, 1938) is an American mathematician specializing in set theory. Biography Solovay earned his Ph.D. from the University of Chicago in 1964 under the direction of Saunders Mac Lane, with a dissertation on '' ...

. His dissertation title was ''Discontinuous Homomorphisms of C''(''Omega'') ''and Set Theory''. He served as

chair A chair is a type of seat, typically designed for one person and consisting of one or more legs, a flat or slightly angled seat and a back-rest. They may be made of wood, metal, or synthetic materials, and may be padded or upholstered in vari ...

of the Berkeley mathematics department for the 2002–2003 academic year. Woodin is a managing editor of the ''

Journal of Mathematical Logic The ''Journal of Mathematical Logic'' was established in 2001 and is published by World Scientific. It covers the field of mathematical logic and its applications. Abstracting and indexing The journal is abstracted and indexed in: * Current Math ...

''. He was elected a Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, a ...

in 2000. He is the great-grandson of William Hartman Woodin, former

Secretary of the Treasury The United States secretary of the treasury is the head of the United States Department of the Treasury, and is the chief financial officer of the federal government of the United States. The secretary of the treasury serves as the principal a ...

Work

He has done work on the theory of generic multiverses and the related concept of

Ω-logic In set theory, Ω-logic is an infinitary logic and deductive system proposed by as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure H_. Just as the axiom of projective determinacy yields a canonic ...

, which suggested an argument that the

continuum hypothesis In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to ...

is either undecidable or false in the sense of mathematical platonism. Woodin criticizes this view arguing that it leads to a counterintuitive reduction in which all truths in the set theoretical universe can be decided from a small part of it. He claims that these and related mathematical results lead (intuitively) to the conclusion that the continuum hypothesis has a

truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Computing In some pro ...

and the Platonistic approach is reasonable. Woodin now predicts that there should be a way of constructing an inner model for almost all known large cardinals, which he calls the Ultimate L and which would have similar properties as

Gödel's constructible universe In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by , is a particular class of sets that can be described entirely in terms of simpler sets. is the union of the constructible hierarchy . It ...

. In particular, the continuum hypothesis would be true in this universe.

Honors

In 2008, Woodin held the

Gödel Lecture The Gödel Lecture is an honor in mathematical logic given by the Association for Symbolic Logic, associated with an annual lecture at the association's general meeting. The award is named after Kurt Gödel and has been given annually since 1990. ...

titled ''The Continuum Hypothesis, the Conjecture, and the inner model problem of one supercompact cardinal.''

References

External links

* *
Home page
at University of California, Berkeley
Woodin's plenary talk at the 2010 International Congress of MathematiciansIncompatible Ω-Complete Theories
(with

Peter Koellner Peter Koellner is Professor of Philosophy at Harvard University. He received his Ph.D from MIT in 2003. His main areas of research are mathematical logic, specifically set theory, and philosophy of mathematics, philosophy of physics, analytic philo ...

), ''

Journal of Symbolic Logic The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by ''Mathematical Reviews'', Zentralb ...

'', Volume 74, Issue 4 (2009), 1155–117

American logicians 20th-century American mathematicians 21st-century American mathematicians 1955 births Living people Fellows of the American Academy of Arts and Sciences University of California, Berkeley alumni University of California, Berkeley faculty Set theorists Tarski lecturers Hausdorff Medal winners Gödel Lecturers {{US-mathematician-stub

Biography

Work

Honors

See also

References

External links